The invention is based on a fuel supply system of the general type described hereafter. A fuel injection system is already known in which fuel injection valves serve to provide the supplementary mixture. However, in such a system, there is the disadvantage, especially at relatively low fuel injection pressures, that the supplementary fuel which is injected is not atomized sufficiently finely, and the course of combustion in the cylinders of the engine is accordingly not optimal. It is also already known to use ultrasonic atomizer nozzles for the purpose of atomizing the fuel, but in that case, the applicability of the system is very limited, because the maximum atomization output is approximately 2.5 liters per hour.